Search found 62 matches
- Mon Nov 11, 2019 1:51 pm
- Forum: Combinatorics
- Topic: Vietnam tst 2004
- Replies: 1
- Views: 41549
Re: Vietnam tst 2004
The equality holds only when $ABCDEF$ is also equiangular. Taking the $\triangle A_1BB_1$, it can be observed that when the perpendicular is dropped from $B$ on to $A_{1}B_{1}$, two right-angled triangles are formed, where the other two angles in each triangle are $30^\circ$ and $60^\circ$. Hence, w...
- Tue Nov 05, 2019 1:48 am
- Forum: Geometry
- Topic: AIME II 2018 problem 4
- Replies: 1
- Views: 49186
Re: AIME II 2018 problem 4
After the tedious calculations, I found the answers to be $a=25$ and $b=6$.
Therefore, $a+b=31$.
But I'm too tired to write the full solution right now. Hopefully, I will post it when I feel like!
Till then, I invite someone else to prove my answer. Good luck!
Therefore, $a+b=31$.
But I'm too tired to write the full solution right now. Hopefully, I will post it when I feel like!
Till then, I invite someone else to prove my answer. Good luck!
- Tue Nov 05, 2019 1:01 am
- Forum: Number Theory
- Topic: Euler's Criterion
- Replies: 3
- Views: 58359
Re: Euler's Criterion
Don't post such half-detailed problems, if you're really hoping for a solution to be posted.
- Tue Nov 05, 2019 12:59 am
- Forum: Number Theory
- Topic: Euler's Criterion
- Replies: 3
- Views: 58359
Re: Euler's Criterion
What are the values of $A$ and $N$?
Usually, $N$ is considered to be the symbol of "Natural Numbers".
But in this case, which Natural number?
Usually, $N$ is considered to be the symbol of "Natural Numbers".
But in this case, which Natural number?
- Tue Nov 05, 2019 12:57 am
- Forum: Combinatorics
- Topic: Turkey TST 2014
- Replies: 7
- Views: 77626
Re: Turkey TST 2014
BTW, I wonder...
This problem was posted over 5 years ago.
And no one posted a solution to this problem in half a decade!!! WOW!!!
This problem was posted over 5 years ago.
And no one posted a solution to this problem in half a decade!!! WOW!!!
- Tue Nov 05, 2019 12:52 am
- Forum: Combinatorics
- Topic: Turkey TST 2014
- Replies: 7
- Views: 77626
Re: Turkey TST 2014
Taking a $n\times n$ chessboard, where $n\equiv 2$ (mod $4$) and experimenting with smaller values of $n$ (like 6 and 10), yields the pattern which is denoted as series $B$ in the solution. From there, the rest was quite straight-forward! :D But yeah, it is actually an elegant problem, primarily bec...
- Tue Nov 05, 2019 12:34 am
- Forum: Combinatorics
- Topic: Turkey TST 2014
- Replies: 7
- Views: 77626
Re: Turkey TST 2014
The first step remains the same: cutting the board in half and denoting the upper-half as $BROWN$ and the lower-half as $GREEN$. Now, two brown worms ($B_1$ and $B_2$) start from the top-left corner; $B_1$ goes to the right and $B_2$ goes to the down direction. Upon reaching the end of the board, $B...
- Mon Nov 04, 2019 11:39 pm
- Forum: Combinatorics
- Topic: Turkey TST 2014
- Replies: 7
- Views: 77626
Re: Turkey TST 2014
The problem can be approached by first cutting the board in half; let the upper-half be called $BROWN$ and the lower-half be called $GREEN$. Now, a pair of brown worms each from the top-left corner move to each of the squares (except the last one) in the diagonal of the LHS $1007\times1007$ square ...
- Mon Nov 04, 2019 9:32 pm
- Forum: Combinatorics
- Topic: Turkey TST 2014
- Replies: 7
- Views: 77626
Re: Turkey TST 2014
The problem can be approached by first cutting the board in half; let the upper-half be called $BROWN$ and the lower-half be called $GREEN$. Now, a pair of brown worms each from the top-left corner move to each of the squares (except the last one) in the diagonal of the LHS $1007\times1007$ square o...
- Thu Oct 31, 2019 9:11 pm
- Forum: Divisional Math Olympiad
- Topic: Feni Higher Secondary 2017 P9
- Replies: 2
- Views: 56988
Re: Feni Higher Secondary 2017 P9
In Dhaka Regional Math Olympiad 2017, the Champion prize in HS category was achieved by students who scored 5 out of 10. And outside Dhaka, they are solving simultaneous equations!!! This is why Dhaka Regional Math Olympiad is considered to be tougher than the National Math Olympiad itself!!! :lol: ...